Holdings: Point processes and coincidences

Point processes and coincidences: contributions to the theory : with applications to statistical optics and optical communication

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Bibliographic Details
Main Author:	Macchi, Odile 1943- (Author)
Other Authors:	Rafler, Mathias (Editor), Zessin, Hans (Translator)
Format:	Thesis Book
Language:	English French
Published:	Nächst Neuendorf Walter Warmuth Verlag 2017
Series:	Classical Lectures
Subjects:	Quantenoptik Punktprozess Hochschulschrift
Online Access:	Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	305 Seiten 21 cm, 397 g
ISBN:	9783944311036 3944311035

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245	1	0	\|a Point processes and coincidences \|b contributions to the theory : with applications to statistical optics and optical communication \|c Odile Macchi ; augmented with a scholion by Suren Poghosyan and Hans Zessin ; English translation: Hans Zessin
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Record in the Search Index

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adam_text	CONTENTS 1 INTRODUCTION 15 1 SOME GENERAL RESULTS 25 2 POINT PROCESSES AND COINCIDENCES 27 2.1 IN TRO D U C TIO N .............................................................................................27 2.2 REGULAR PROCESSES AND COINCIDENCE D E N S IT IE S .......................... 28 2.2.1 ASSUMPTIONS FOR ORDERLY PROCESSES ............................................ 28 2.2.2 COINCIDENCE AND EXCLUSION PROBABILITIES ................................... 30 2.3 SHOT NOISE P RO C E S S E S ...........................................................................34 2.3.1 DEFINITION.........................................................................................34 2.3.2 CHARACTERISTIC FUNCTION OF ORDER Q ............................................ 35 2.3.3 JOINT DISTRIBUTION OF COUNTING V A RIA B LE S ................................... 37 2.4 EXCLUSION D E N S ITIE S .......................... 41 2.4.1 EXCLUSION (PROBABILITY) DENSITIES.................................................41 2.4.2 DISTANCES BETWEEN INSTANTS AND IMPULSES ............................... 42 2.4.3 INTERVALS BETWEEN NEIGHBOURING IM PULSES ............................... 43 2.4.4 SURVIVALTIME AND LIFETIME.............................................................. 44 2.5 S TA TIO N A R ITY ............................................................................................. 45 2.6 OPERATIONS ON POINT P RO C E S S E S ..........................................................47 2.6.1 SUPERPOSITION ................................................................................ 47 2.6.2 RANDOM THINNING............................................................................49 2.7 E X A M P LE S ..................................................................................................49 2.7.1 THE POISSON P RO C E S S ................................................................... 49 2.7.2 DETECTION OF A MONO-MODE FIELD WITH N PHOTONS ...................... 51 2.A ADDITIONAL P RO O FS ....................................................................................54 LAWS OF REGULAR POINT PROCESSES 57 3.1 THE SPACE OF RE A LIZ A TIO N S ...................................................................57 3.1.1 SYMMETRIC SETS IN 3N.................................................................. 58 3.2 E V E N T S ...................................................................................................... 58 3.2.1 THE COUNTING A LG E B RA ................................................................... 59 3.2.2 DISTRIBUTIONS OF P ELEM ENTS .......................................................... 62 3.3 PROBABILITY L A W S .................................................................................... 67 3.3.1 EXCLUSION PROBABILITIES................................................................... 68 3.3.2 SYMMETRY OF L A W S ....................................................................... 69 3.3.3 COINCIDENCE P RO B A B ILITIE S .......................................................... 71 3.3.4 PROBABILITIES OF CYLINDERS IN AND ....................................74 3.3.5 MOMENTS AND FACTORIAL MOMENTS ................................................. 75 3.4 REGULAR POINT PROCESSES....................................................................... 80 3.4.1 DENSITIES OF EXCLUSION P RO B A B ILITIE S ........................................ 80 3.4.2 COINCIDENCE PROBABILITY D E N S ITIE S .............................................82 3.4.3 CONSTRUCTION OF POINT PROCESSES ................................................. 67 3.5 A-FINITE POINT P RO C E S S E S ....................................................................... 91 3.5.1 EXCLUSION PROBABILITIES................................................................... 92 3.5.2 COINCIDENCE DENSITIES................................................................... 93 3.6 CHARACTERISTIC FU N C TIO N A LS ...................................................................96 II POINT PROCESS MODELS 101 4 COX PROCESSES AND PHOTOELECTRONS 103 4.1 IN TRO D U C TIO N ........................................................................................... 103 4.2 DETECTION OF AN OPTICAL F I E L D ............................................................ 104 4.3 THE COX P RO C E S S .................................................................................. 106 4.3.1 DEFINITION.......................................................................................106 4.3.2 CHARACTERISTIC AND GENERATING FU N C TIO N ................................. 108 4.3.3 EXCLUSION PROBABILITIES ................................................................ 110 4.3.4 STATIONARITY.................................................................................. 112 4.3.5 SUPERPOSITION AND THINNING........................................................112 4.4 THERM AL L I G H T .......................................................................................113 4.4.1 INTRODUCTION.................................................................................. 113 4.4.2 THE GENERATING FUNCTION OF IM PU LSES ...................................... 114 4.4.3 THE METHOD OF COINCIDENCES ................................................... 115 4.4.4 EXCLUSION PROBABILITIES.................................................................116 4.4.5 EXAMPLE: THERMAL LIGHT WITH LORENTZ-SPECTRUM .................... 119 4.5 THE DOUBLY STOCHASTIC POISSON P R O C E S S ...................................... 122 4.5.1 JOINT LAWS.......................................................................................122 4.5.2 COINCIDENCES..............................................................................123 4.6 THE GAUSS-POISSON P RO C E S S ............................................................ 125 4.6.1 M O TIV A TIO N .................................................................................. 125 4.6.2 THE CHARACTERISTIC FUN CTIO N AL ................................................... 125 4.6.3 COINCIDENCES..............................................................................129 4.6.4 EXCLUSION PROBABILITIES AND AN EXISTENCE THEOREM. . . . 130 4.6.5 THE STATIONARY CASE..................................................................... 132 4.6.6 AN EXAMPLE.................................................................................. 133 4.6.7 PROOF OF THEOREM 4 . 4 ................................................................ 134 4 .A PROOF OF FORMULA ( 4 . 6 6 ) .....................................................................135 5 RENEWAL PROCESSES 139 5.1 D E FIN ITIO N ................................................................................................139 5.2 EXCLUSION PROBABILITIES ......................................................................... 140 5.3 JOINT COUNTING LA W S ..............................................................................141 6 FERMIONS IN A CHAOTIC STATE 145 6.1 IN TRO D U C TIO N ............................................................................................145 6.2 CHARACTERIZATION OF FERM IONS.............................................................146 6.2.1 GENERALITIES...................................................................................146 6.2.2 GENERATING FUNCTION OF THE COUNTING V A R IA B LE S .................... 147 6.2.3 NECESSARY AND SUFFICIENT CONDITIONS FOR G TO BE A GENER ATING FU N CTIO N .............................................................................. 150 6.2.4 A BASIC THEOREM..........................................................................155 6.3 FERMIONS IN A CHAOTIC STATE: PHYSICAL POINT OF VIEW .... 162 6.3.1 INTRODUCTION...................................................................................162 6.3.2 THE M O D E S ...................................................................................162 6.3.3 DENSITY MATRICES. EMISSION AND DETECTION PROCESSES . .163 6.3.4 D ISCUSSION...................................................................................165 6.4 AN ANALOGY BETWEEN CHAOTIC BEAM S OF FERMIONS AND OF B O S O N S ................................................................. 168 6.5 AN E X A M P LE ............................................................................................170 6.5.1 INTRODUCTION...................................................................................170 6.5.2 IS A GENERALIZED RENEWAL PROCESS ...................................... 170 6.5.3 LORENTZIAN ASSUMPTIONS ............................................................ 172 III OPTICAL COMMUNICATIONS 175 7 WEAK OPTICAL SIGNALS 177 7.1 IN TRO D U C TIO N ............................................................................................177 7.2 ESTIMATION OF A MODULATED OPTICAL S IG N A L ...................................... 178 7.2.1 THE P R O B LE M .............................................................................. 178 7.2.2 GENERAL R E S U LT S ..........................................................................179 7.2.3 THE CASE OF WEAK N O IS E .............................................................182 7.2.4 AN EXAM PLE...................................................................................184 7.3 ESTIMATION OF THE INTENSITY OF THERM AL L I G H T .................................. 188 7.4 LINEAR ES TIM A TIO N ................................................................................... 193 7.4.1 INTERNAL NOISE OF THE D ETECTO R....................................................194 7.4.2 NOISE FROM PARASITICAL RADIATION ............................................... 196 7.5 DETECTION P RO B LE M S ..............................................................................199 7.5.1 THERMAL NOISE OF THE DETECTOR.................................................200 7.5.2 PARASITICAL ENVIRONMENTAL RADIATION .......................................... 203 7.5.3 FINAL REM ARKS ................................... 205 7.6 C O N C LU S IO N S ...........................................................................................206 7 .A SOM E GENERAL PROPERTIES OF THE ESTIMATORS .................................... 207 7.A.1 EXPECTATION OF AQ{TN} ................................................................ 207 7.A.2 VARIANCE OF AQ{TN) .........................................................................208 7.A.3 PROOF OF FORMULA (7.19) ............................................................209 7.B THE R E S O LV E N T ..................................................................................... 210 IV LATER MATHEMATICAL DEVELOPMENTS 215 8 QUANTUM-CLASSICAL PROCESSES 217 8.1 IN TRO D U C TIO N ...........................................................................................218 8.1.1 SOME MATHEMATICAL T O O L S ....................................................... 223 8.2 A GENERAL CONSTRUCTION S C H E M E ....................................................... 225 8 . 2.1 NEHRING*S REPRESENTATION OF 3 L ...............................................227 8.3 A SPECIAL CLASS OF FUNCTIONALS L ....................................................... 229 8.3.1 GLOBAL ASSUMPTIONS ON THE POTENTIALS......................................234 8.3.2 INFINITELY EXTENDED PROCESSES...................................................237 8.3.3 EXPLICIT CONDITIONS FOR THE P O TE N TIA LS ......................................239 8.4 THE CLUSTER E Q U A T IO N ......................................................................... 240 8.4.1 A GENERAL PRINCIPLE IMPLYING A COX STRUCTURE ........................ 242 8.5 FACTORIAL MOMENT M E A S U R E S ............................................................244 8.6 A REPRESENTATION OF THE MODIFIED LAPLACE TRANSFORM .... 246 9 QUANTUM PROCESSES 247 9.1 CONSTRUCTION OF QUANTUM PROCESSES...............................................247 9.1.1 A CONSTRUCTION METHOD INDUCING QUANTUM INTERACTIONS . . 249 9.2 IMMANANTAL P R O C E S S E S .....................................................................250 9.3 COX P RO C E S S E S ...................................................................................... 253 9.4 SUPPORT P RO P E R TIE S ..............................................................................254 9.5 GIBBSIAN C H A RA C TE R.............................................................................. 255 9.6 INVARIANCE PROPERTIES AND LAWS OF LARGE N U M B E R S .................... 256 9 .7 MIXING OF QUANTUM P R O C E S S E S ........................................................259 9.8 A CENTRAL LIMIT THEOREM FOR QUANTUM P RO C E S S E S .........................262 10 EXAMPLES OF QUANTUM PROCESSES 265 10.1 QUANTUM COX P R O C E S S E S .................................................................267 10.1.1 THERMAL LIGHT. THE PHOTON PROCESS .......................................... 267 10.2 QUANTUM POLYA P RO CESSES.................................................................269 10.2.1 PE IS A PAPANGELOU P RO C E S S ................................................... 270 10.3 IDEAL BOSONS AND F E R M IO N S ............................................................ 272 10.3.1 LAWS OF LARGE NUMBERS AND CENTRAL LIMIT THEOREMS. . . .273 10.3.2 CLUSTERING REPRESENTATION OF 5+ ............................................... 274 10.4 QUANTUM RENEWAL P RO CESSES ............................................................ 275 10.5 GINIBRE P R O C E S S E S .............................................................................. 276 10.5.1 THE EXPONENTIAL KERNEL IS A QUANTUM INTERACTION . . . .276 10.5.2 C O N STRU CTIO N .............................................................................. 278 10.5.3 GIBBSIAN AND COXIAN CH A RA C TE R............................................... 279 10.5.4 ASYMPTOTIC BEHAVIOUR.................................................................279 11 PRESSURE OF QUANTUM SYSTEMS 283 11.1 THE P RO B LE M ............................................................................................283 11.1.1 A DECOMPOSITION..........................................................................284 11.1.2 THE SECOND TERM ..........................................................................285 11.2 E X A M P LE S ................................................................................................286 11.2.1 POLYA PROCESSES..........................................................................286 11.2.2 GINIBRE P RO C E S S E S ..................................................................... 286 11.2.3 IDEAL BOSONS AND FERMIONS IN THE COMPLEX PLANE .... 238 BIBLIOGRAPHY 291
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spelling	Macchi, Odile 1943- Verfasser (DE-588)1136310541 aut Macchi, Odile Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication Odile Macchi ; augmented with a scholion by Suren Poghosyan and Hans Zessin ; English translation: Hans Zessin Nächst Neuendorf Walter Warmuth Verlag 2017 305 Seiten 21 cm, 397 g txt rdacontent n rdamedia nc rdacarrier Classical Lectures Dissertation Université de Paris Sud 1972 unter dem Titel: Processus ponctuels et coincidences Quantenoptik (DE-588)4047990-0 gnd rswk-swf Punktprozess (DE-588)4138173-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Punktprozess (DE-588)4138173-7 s Quantenoptik (DE-588)4047990-0 s DE-604 Rafler, Mathias (DE-588)1155326121 edt Zessin, Hans (DE-588)1136330453 trl Poghosyan, Suren (DE-588)1136343083 oth Dr. Walter Warmuth (Firma) (DE-588)1067142398 pbl B:DE-101 application/pdf http://d-nb.info/1133503438/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030275023&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Macchi, Odile 1943- Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication Quantenoptik (DE-588)4047990-0 gnd Punktprozess (DE-588)4138173-7 gnd
subject_GND	(DE-588)4047990-0 (DE-588)4138173-7 (DE-588)4113937-9
title	Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication
title_alt	Macchi, Odile
title_auth	Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication
title_exact_search	Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication
title_full	Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication Odile Macchi ; augmented with a scholion by Suren Poghosyan and Hans Zessin ; English translation: Hans Zessin
title_fullStr	Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication Odile Macchi ; augmented with a scholion by Suren Poghosyan and Hans Zessin ; English translation: Hans Zessin
title_full_unstemmed	Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication Odile Macchi ; augmented with a scholion by Suren Poghosyan and Hans Zessin ; English translation: Hans Zessin
title_short	Point processes and coincidences
title_sort	point processes and coincidences contributions to the theory with applications to statistical optics and optical communication
title_sub	contributions to the theory : with applications to statistical optics and optical communication
topic	Quantenoptik (DE-588)4047990-0 gnd Punktprozess (DE-588)4138173-7 gnd
topic_facet	Quantenoptik Punktprozess Hochschulschrift
url	http://d-nb.info/1133503438/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030275023&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT macchiodile macchiodile AT raflermathias macchiodile AT zessinhans macchiodile AT poghosyansuren macchiodile AT drwalterwarmuthfirma macchiodile AT macchiodile pointprocessesandcoincidencescontributionstothetheorywithapplicationstostatisticalopticsandopticalcommunication AT raflermathias pointprocessesandcoincidencescontributionstothetheorywithapplicationstostatisticalopticsandopticalcommunication AT zessinhans pointprocessesandcoincidencescontributionstothetheorywithapplicationstostatisticalopticsandopticalcommunication AT poghosyansuren pointprocessesandcoincidencescontributionstothetheorywithapplicationstostatisticalopticsandopticalcommunication AT drwalterwarmuthfirma pointprocessesandcoincidencescontributionstothetheorywithapplicationstostatisticalopticsandopticalcommunication

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